What is 2ln(x-1)-1/2 ln(y)-3ln(y) ?

The solution to 2ln(x-1)-1/2 ln(y)-3ln(y) is ln((sqrt(y)(x-1)^2)/(y^4))

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simplify 2ln(x-1)-1/2 ln(y)-3ln(y)

simplify

2 ln (x - 1) - \frac{1}{2} ln (y) - 3 ln (y)

ln (\frac{y ( x - 1 ) ^{2}}{y ^{4}})

Solution steps

2 ln (x - 1) - \frac{1}{2} ln (y) - 3 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x - 1) = ln ((x - 1)^{2})

= ln ((x - 1)^{2}) - \frac{1}{2} ln (y) - 3 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (y) = ln (y^{\frac{1}{2}})

= ln ((x - 1)^{2}) - ln (y^{\frac{1}{2}}) - 3 ln (y)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((x - 1)^{2}) - ln (y^{\frac{1}{2}}) = ln (\frac{( x - 1 ) ^{2}}{y ^{\frac{1}{2}}})

= ln (\frac{( x - 1 ) ^{2}}{y ^{\frac{1}{2}}}) - 3 ln (y)

Simplify

\frac{( x - 1 ) ^{2}}{y ^{\frac{1}{2}}} : \frac{y ( x - 1 ) ^{2}}{y}

= ln (\frac{y ( x - 1 ) ^{2}}{y}) - 3 ln (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (y) = ln (y^{3})

= ln (\frac{y ( x - 1 ) ^{2}}{y}) - ln (y^{3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (\frac{y ( x - 1 ) ^{2}}{y}) - ln (y^{3}) = ln \frac{\frac{y ( x - 1 ) ^{2}}{y}}{y ^{3}}

= ln \frac{\frac{y ( x - 1 ) ^{2}}{y}}{y ^{3}}

Simplify

\frac{\frac{y ( x - 1 ) ^{2}}{y}}{y ^{3}} : \frac{y ( x - 1 ) ^{2}}{y ^{4}}

= ln (\frac{y ( x - 1 ) ^{2}}{y ^{4}})

ln (\frac{tan ^{2} ( x )}{e ^{4 x^{2}} ∣ x ^{5} ∣})

ln (e^{- 9 θ} \frac{θ ^{9}}{9 !})

\frac{1}{2} ln (x) + 3 ln (2)

ln (p^{4}) + ln (3 p^{5}) - 2 ln (x)

3 (\frac{14}{3}) - 14 ln (7 (\frac{14}{3}))

What is 2ln(x-1)-1/2 ln(y)-3ln(y) ?
The solution to 2ln(x-1)-1/2 ln(y)-3ln(y) is ln((sqrt(y)(x-1)^2)/(y^4))